# A Practical Introduction to Bayesian Estimation of Causal Effects: Parametric and Nonparametric Approaches

arXiv: https://arxiv.org/abs/2004.07375 · HTML: https://mlsanity.com/paper/2004.07375/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [Causal Foundation Models with Continuous Treatments](https://mlsanity.com/paper/2605.15133/) (2026)
- [Interventional Processes for Causal Uncertainty Quantification](https://mlsanity.com/paper/2410.14483/) (2024)
- [Improving Generative Methods for Causal Evaluation via Simulation-Based Inference](https://mlsanity.com/paper/2509.02892/) (2025)

## Abstract (arXiv)

Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian models and would like an overview of what it can add to causal estimation in practical settings. In the paper, we demonstrate how priors can induce shrinkage and sparsity on parametric models and be used to perform probabilistic sensitivity analyses around causal assumptions. We provide an overview of nonparametric Bayesian estimation and survey their applications in the causal inference literature. Inference in the point-treatment and time-varying treatment settings are considered. For the latter, we explore both static and dynamic treatment regimes. Throughout, we illustrate implementation using off-the-shelf open source software. We hope the reader will walk away with implementation-level knowledge of Bayesian causal inference using both parametric and nonparametric models. All synthetic examples and code used in the paper are publicly available on a companion GitHub repository.